Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man (25 page)

Encore

A
lthough Chapter 4 presented a variety of evidence that the structure of music has the signature of human movers, there is additional evidence that couldn’t reasonably be fit into that chapter, and so it appears here in the Encore.

1
The Long and Short of Hit

The mysterious approaching monster from the section titled “Backbone” in Chapter 4 was mysterious because you mistakenly perceived a hit sound rapidly following the footstep; that is, you perceived the between-the-steps interval to be split into a short interval (from step to rapidly following hit) and a long interval (from that quick post-step hit to the next footstep). The true gait of the approaching lilting lady had its between-the-steps interval broken, instead, into a long interval followed by a short interval. My attribution of mystery to the “short-long” gait, not the “long-short,” was not arbitrary. “Short-long”
is
a strange human gait pattern, whereas “long-short” is commonplace.

Your legs are a pair of 25-pound pendulums that swing forward as you move, and are the principal sources of your between-the-steps hit sounds. A close look at how your legs move when walking (see Figure 41) will reveal why between-the-step hits are more likely to occur just
before
a footstep than just after. Get up and take a few steps. Now try it in slow motion. Let your leading foot hit the ground in front of you for its step. Stop there for a moment.
This
is the start of a step-to-step interval, the end of which will occur when your now-trailing foot makes
its
step out in front of you. Before continuing your stride, ask yourself what your trailing foot is doing. It isn’t doing anything. It is on the ground. That is, at the start of a step-to-step interval,
both
your feet are planted on the ground. Very slowly continue your walk, and pay attention to your trailing foot. As you move forward, notice that your trailing foot stays planted on the ground for a while before it eventually lifts up. In fact, your trailing foot is still touching the ground for about the first 30 percent of a step-to-step interval. And when it finally does leave the ground, it initially has a very low speed, because it is only just
beginning
to accelerate. Therefore, for about the first third of a step, your trailing foot is either not moving or moving so slowly that any hit it does take part in will not be audible. Between-the-footsteps hit sounds are thus relatively rare immediately after a step. After this slow-moving trailing-foot period, your foot accelerates to more than
twice
your body speed (because it must catch up and pass your body). It is during this central portion of a step cycle that your swinging leg has the energy to really bang into something. In the final stage of the step cycle, your forward-swinging leg is decelerating, but it still possesses considerable speed, and thus is capable of an audible hit.

Figure 41
. Human gait. Notice that once the black foot touches the ground (on the left in this figure), it is not until the next manikin that the trailing (white) foot lifts. And notice how even by the middle figure, the trailing foot has just begun to move. During the right half of the depicted time period, the white leg is moving quickly, ready for an energetic between-the-steps hit on something.

We see, then, that there is a fundamental temporal asymmetry to the human step cycle. Between-the-steps hits by our forward-swinging leg are most probable at the middle of the step cycle, but there is a bias toward times nearer to the later stages of the cycle. In Figure 41, this asymmetry can be seen by observing how the distance between the feet changes from one little human figure to the next. From the first to the second figure there is no change in the distance between the feet. But for the final pair, the distance between the feet changes considerably. For human gait, then, we expect between-the-steps gangly hits as shown in Figure 42a: more common in mid-step than the early or late stages, and more common in the late than the early stage.

Figure 42
.
(a)
Because of the nature of human gait, our forward-swinging leg is most likely to create an audible between-the-steps bang near the middle of the gait cycle, but with a bias toward the late portions of the gait cycle, as illustrated qualitatively in the plot.
(b)
The relative commonness of between-the-beat notes occurring in the first half (“early”), middle, or second half (“late”) portions of a beat cycle. One can see the qualitative similarity between the two plots.

Does music show the same timing of when between-the-beat notes occur? In particular, are between-the-beat notes most likely to occur at about the temporal center of the interval, with notes occurring relatively rarely at the starts and ends of the beat cycle? And, additionally, do we find the asymmetry that off-beat notes are more likely to occur late than early (i.e., are long-shorts more common than short-longs)? This is, indeed, a common tendency in music. One can see this in the classical themes as well, where I measured intervals from the first 550 themes in Barlow and Morgenstern’s dictionary, using only themes in
4
/
4
time. There were 1078 cases where the beat interval had a single note directly in the center, far more than the number of beat intervals where only the first or second half had a note in it. And the gaitlike asymmetry was also found: there were 33 cases of “short-longs” (beat intervals having an off-beat note in the first half of the interval but not the second half, such as a sixteenth note followed by a dotted eighth note), and 131 cases of “long-shorts” (beat intervals having a note in the second half of the interval but not the first half, like a dotted eighth note followed by a sixteenth note). That is, beat intervals were four times more likely to be long-short than short-long, but both were rare compared to the cases where the beat interval was evenly divided. Figure 42b shows these data.

Long-shorts are more common in music because they perceptually feel more natural for movement—because they
are
more natural for movement. And, more generally, the time between beats in music seems to get filled in a manner similar to the way ganglies fill the time between steps. In the Chapter 4 section titled “The Length of Your Gangly,” we saw that beat intervals are filled with a human-gait-like
number
of notes, and now we see that those between-the-beat notes are positioned inside the beat in a human-gait-like fashion.

Thus far in our discussion of rhythm and beat, we have concentrated on the temporal pattern of notes. But notes also vary in their emphasis. As we mentioned earlier, on-beat notes typically have greater emphasis than between-the-beat notes, consistent with human movers typically having footsteps more energetic than their other gangly bangs. But even notes on the beat vary in their emphasis, and we take this up next.

2
Measure of What?

Thus far we have discussed beats as footsteps, and between-the-beat notes as between-the-footsteps banging ganglies. But there are other rhythmic features of music that occur at the scale of
multiple
beats. In particular, music rarely treats each and every beat as equal. Some beats are special. In ¾ time, for example, every third beat gets a little emphasis, and in
4
/
4
time every fourth beat gets an emphasis. This is the source of the
measure
in music, where the first beat in each measure gets the greatest emphasis. (And there are additional patterns: in
4
/
4
time, for instance, the third beat gets a little extra oomph, too, roughly half that of the first.) If you keep the notes of a piece of music the same, but modify which beats are emphasized, the song can often sound nearly unrecognizable. For example, here is “Twinkle, Twinkle Little Star,” but with some unusual syllables emphasized to help you sing it in ¾ time rather than the appropriate
4
/
4
time. “
TWI
-nkle, twi-
NKLE
, lit-tle
STAR
, , how
I
won-der
WHAT
you are.” As you can see, it is very challenging to even get yourself to sing it in the wrong time signature. And when you eventually manage to do it, it is a quite different song from the original.

Why should a difference in the pattern of emphasis on beats make such a huge difference in the way music sounds to us? With the movement theory of music in hand, the question becomes: does a difference in the pattern of emphasis of a mover’s footsteps make a big difference in the meaning of the underlying behavior? For example, is a mover with a ¾ time gait signature probably doing a different behavior than a mover with a
4
/
4
time gait signature?

The answer is, “Of course.” A different pattern in footstep emphasis means the mover is shifting his body weight in a different pattern. The ¾ time mover has an emphasis on every third step, and thus alternates which foot gets the greater emphasis. The 4/4 time mover, on the other hand, has emphasis on every other step, with extra emphasis on every fourth step. These are the gait sounds of distinct behaviors. Real movements by people may not stay within a single time signature for prolonged periods, as music often does, but, instead, change more dynamically as the mover runs, spins, and goes up for a layup. Time-signature differences in movement imply differences in behavior, and so we expect that our auditory system is sensitive to these time signatures . . . and that music may have come to harness this sensitivity, explaining why time signature matters in music.

And notice that when we hear music with a time signature, we want to move consistently not only with the beat and the temporal pattern of notes, but
also
with the time signature. People
could
waltz to music with a
4
/
4
time signature, but it just does not feel right. People not only want to step to the beat, (something we discussed early in Chapter 4); they want to step extra hard on the emphasized beat.

This and the previous Encore section concerned rhythm. The upcoming two also concern rhythm, and how it interacts with melody and with loudness, respectively.

3
Fancy Footwork

When the kids and I are doing donuts in the parking lot at the dollar store—that is, driving the minivan in such tight circles that the wheels begin to screech and squeal—we are making minivan gangly banging sounds. Such behavior leads to especially complex rubber-meets-road hits and slides, sounds we revel in as we’re doing it. But the patrons at the dollar store hear an additional feature. The patrons hear Doppler shifts, something that the kids and I do not hear because we are stationary relative to the minivan. For the dollar store patrons, the pitch of the envelope of minivan gangly bangings rises and falls as we approach and recede from them in our donuts. In fact, it is
because
my minivan is veering so sharply that its ganglies begin banging in a more complex fashion. Compared to minivans
not
doing donuts, minivans doing donuts change pitch faster
and
have more complex “gaits.” Greater pitch changes therefore tend to be accompanied by more complex gait patterns.

This pitch-rhythm connection is also found among human movers. When we turn, we are likely to have a more complex gait and gangly pattern than when we are simply moving straight ahead. For example, when you turn left, you must lean left, lest you fall over on your right side; and your legs can no longer simply swing straight past each other, but must propel the body leftward via a push or pivot. And many turns involve more complex footwork, such as sidestepping, trotting, twists, and other maneuvers we acrobatic apes regularly carry out. For example, when a basketball player crosses the court, his or her path is roughly straight, and the resultant gait sounds are a simple beat. Once a player has crossed the court, however, his or her movements tend to be curvy, not straight, as players on offense try to free themselves up for a pass, or players on defense loom in for a steal or shadow the offense to prevent a pass, in each case setting off a richer pattern of gangly sounds.

Does music behave in this way? When melodic pitches change—a signal that the depicted mover is turning, as we discussed in Chapter 4—does the rhythm tend to get more complex? As a test for this, I sampled 713 two-beat intervals having at least two notes each from the
Dictionary of Musical Themes
, and for each recorded whether the pitch was varying or unvarying, and whether the rhythm was simple (one note on each beat, or “just the footsteps”) or complex (more than “just the footsteps”). (Data were sampled from
2
/
4
and
4
/
4
time signature pieces, and from every tenth theme up to “D400” in the Dictionary.) When pitch changed over the two-beat intervals, the probability was 0.66 that the beat was complex, whereas when pitch did not change the probability was only 0.35 that the beat was complex. Consistent with the prediction from real-world turners, then, these data suggest that when music changes pitch—the Doppler signature of a mover changing direction—its rhythm tends to become more complex. That is, as with people, when music “turns,” the ganglies start flying.

We see, then, that melody interacts with rhythm in the way Doppler interacts with gait. Now let’s ask whether loudness also interacts with rhythm, as expected from the ecology of human movers. We take that up in the next Encore section.

4
Distant Beat

As I write this I am on the (inner) window ledge of my office at RPI, overlooking downtown Troy and the Hudson River. I’m on the fifth floor (of the city side of the building), with a steep, sloping hill at the bottom, so everything I hear is either fairly far away, or very far away. Because of my extreme distance from nearly everything, I end up hearing only a small sample of the sounds occurring in the city. Mainly, I hear the very energetic events. If a sound were not very energetic, then it would be inaudible by the time the sound waves reached me. I can see a tractor dumping rocks, but I hear only the boom of a particularly large one, missing out on the sounds of the many smaller rock hits I can see but cannot hear. Generally, when something makes complex sounds, whether it is a car, a washing machine, or a tornado, some of the noises composing the whole are more energetic than others. If it is far away from you, then you will only hear the most energetic parts of the sound. But if you are close, you’ll be able to hear the full panoply of sounds.

As with most complex sound makers, human movers make sounds of varying energy and frequency. The most energetic sounds tend to be our footsteps. Accordingly, the first thing we hear when someone is approaching from afar tends to be their footsteps. The other gait-related sounds from clanging limbs are difficult to hear when far away, but they get progressively more audible as the mover nears us. That is, as a mover gets closer to us and the loudness of his gait sounds thereby rises, the number of audible gait sounds per footstep tends to increase.

If music has culturally evolved to sound like human movement, then we accordingly expect that the louder parts of songs should have more notes per beat (i.e., more fictional gangly bangs per step). Do they? Do
fortissimo
passages have greater note density than
pianissimo
? Caitlin Morris, as an undergraduate at RPI, set out to test this among scores in
An Anthology of Piano Mu
s
ic, Vol. II: The Classical Period
, by Denes Agay (New York: Music Sales America, 1992), and found that this is indeed the case. Figure 43 shows how the density of notes (the number of notes per beat) varies with loudness over 60 classical pieces. One can see that note density increases with loudness, as predicted. Music doesn’t have to be like this. Music
could
pack more notes in per beat in soft parts, and have only on-the-beat notes for the loud parts. Music has this louder-is-denser characteristic because, I submit,
that’s
a fundamental
ecological
regularity our auditory systems have evolved to expect for human (and any) movers.

This result is, by the way, counter to what one might expect if loudness were due not to spatial proximity but to the energy level (or “stompiness,” as we discussed in the Chapter 4 section titled “Nearness versus Stompiness”) of the mover. Louder stomps typically require longer gaps between each stomp. “Tap, tap, tap, tap, tap” versus “BANG!  . . . . . . . . BANG!”

Now that we have expanded on rhythm, we will move on to further evidence that melodic contour acts as Doppler pitch.